ChatGPT doesn't use the API. It uses the same underlying model with a bunch of added prompts (and possibly additional fine-tuning?) to add to make it conversational.
One would pay because what they get out of chatGPT provides value, of course. Keep in mind that the users of these 2 products can be (and in fact are) different — chatGPT is a lot friendlier (from a UX perspective) than using the API playground (or using the API itself).